eiz 5. Evaluate dz, where; (z+2)²(z-1) (a) y is the circle |z| = 1/2 traversed once counterclockwise; (b) y is the circle |z| = 3/2 traversed once counterclockwise; (c) y is the circle |z| = 3 traversed once counterclockwise;

Q: F. Prove the following: (10 pts each) 1.

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Q: b) Simplify the following equation using positive indices only 3 3(3x+2)4(2x+0.5) 2(2x-5)9(2x-2)

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A: Area of Medium rectangle= 10 *Area of small square. Area of Large square =  10 *Area of medium…

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A: f(x) = xlnx -x Here the product rule applied on the term (x lnx) only. f'(x) = d/dx (xlnx) + d/dx…

Q: 2. Evaluate z²+1 Z (a) J₁2-2 (2-13dz. (b) √₁2-2|=1 (2²-4)²· √3dz.

A: The given problem is to evaluate the given complex integrals over the given counter of region. We…

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A: For the given indefinite integral, the first step in evaluation of this integral is:

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Q: Z = i+1 then find fourth root

A: Here the equation is given by Z=i+1. The fourth root of the equation has to be determined.

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Q: How were algebraic structures discovered?

A: This transcend through history of some brilliant mathematical genius who could find pattern in…

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A: see below the answer

Q: 2 2(3)' Find: i=1

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Q: 8. Evaluate (a) J₁2-2 22+2+d; (b) J₁2-22²-22-3dz

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Q: I really needed

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Q: -1 0 -6 9- Let D = 4 Find -2D = 2.

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Q: Describe the steps in words that you would use to show that (x - a) is a factor of x" - a". Your…

A: Let f(x)=xn-an. Now using binomial expansion…

Q: Describe the steps in words that you would use to show that (x - a) is a factor of x" - a". Your…

A: Introduction: A statement P(n), where n is a natural number, is an example. Then, employ the…

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A:

Q: 559 [(-36) ³1³: [(-3) 5 (-2)51³}: {(-36) ¹2 : [(+6) 312³310

A: Given: The expression is -+18:-623:-45:-5. Simplify the given expression. Formula used: The…

Q: Please explain this with more focus on the theory

A: Given that the number of defects in a sheet of rolled steel follows a Poisson distribution, we can…

Q: Evaluate using any method you want: 32 - 16 dz

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Q: Evaluate: [8zº · sec² (25) dx =

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Q: 2.2 Simplify the complex power ()-“ and leave your answer in its simplest form.

A: Given 1+i1-i-2i

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Q: olve the equation by the method of your choice. V2x? + 3x-92 = 0 The solution set is }. Simplify…

A:

Q: the velumg of a Gale ungtrude) finm a agn by Caffing tolume of 54d a Tozt Ximia laca of Card toud…

A: We need to maximize volume.

Q: 4Q Express 2= (1+2i)² 7-i in the form a + ib where a and b are real numbers.

A:

Q: Evaluate for r= (- 2,0), s = (- 5, – 1), and t= (-4,1). 2r - (s + t) = (OD (Simplify your answers.)

A: To find:2r-s+tr=-2, 0, s=-5, -1, t=-4, 1

Q: What other applications do Numerical Analysis is used? Clearly explain how Numerical Analysis used…

A: To determine: Applications of Numerical Analysis and to explain how Numerical Analysis is used in…

Q: y%=x(x2 +x- 2) 3

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Q: (2) Write an expression to represent the area of the triangle: 2y²-2y 3 3y-30 4y² A) (-10)(y-1) B)…

A:

Q: Evaluate. Show all your work and make sure answer is in simplest form. 1 dx (9+16x*) 9+16x² )

A: ∫tn dt =tn+1n+1+C ∫cos(at) dt =1asin(at)+C

Q: 4 y = f(x) 5-4 3 -2 -1 -1+ -2 5, 3. 2.

A: according to given figure limx→4fx=4f-3=-2f'4=0 here, given function is not continuous at x=-3  so,…

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Q: * lif z= 4i / (-3-4i) , find |z

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Q: x2 x*(a² + x²)% dx = 1 (a² + x²)7 + C 15 3

A: We use substitution method